Algorithm Research On C-C Subdivision Of C-B Spline

Surface subdivision is a new type of discrete modeling method appearing in the recent years, that is, the method for producing curve and surface by applying pre-set subdivision rules to the initial control grid. The subdivision surface method is a powerful tool of geometric modeling technique and has not only the advantages of affine invariance and local support B-Spline surface has, but also the arbitrary topology which the parametric surface doesn't have. At present, there are many different kinds of subdivision modes. C-C subdivision mode is a generalization of B-spline, which is better combined with BURBS curve and can be better combined with NC machining. Taking C-B spline as the breakthrough point, C-B spline-based C-C subdivision algorithm is obtained through the analysis and research of the C-B spline curve, and applying C-B spline to C-C subdivision curve and surface. At the same time, the adaptive subdividing method is taken to improve modeling ability of subdivision curves and surfaces on the basis of studying new algorithms. The modelling technology of subdivision curves and surfaces is studied from the view of applications. The content of the paper is as follows:Firstly, the situation of subdivision curves and surfaces, the basic principles, characteristics and classifications were introduced. The basic principle and algorithm of C-C subdivision mode, D-Sabin subdivision mode and Loop subdivision mode are especially discussed.Secondly, the characteristics of C-B spline curve and surface is analyzed on the basis of studying C curve surface, for example, using C-B spline curve to precisely show the circular arc and ellipse arc and so on. Apply the result to the curved surface, that is, using the C-B spline curve to construct the common engineering surfaces. Then, the characteristics of C-B spline are applied to C-C subdivision surface to construct a new subdivision algorithm at the singular point, to make produced subdivision surface not only adjustable in C-B spline range but also arbitrary adjustment between standard C-C subdivision surface and initial control grid feasible.Finally, the impact of adaptive subdivided method on the continuities of curve surface grid is thought. And adaptive methods based on surface pieces were studied. According to the definition of adaptive subdivided criterion, the different segments of criteria were used to C-C segmentation mode and C-C subdivision mode of C-B spline and corresponding adaptive new algorithms are obtained respectively. Solved The problem of the excessive thinning division during the subdivision is solved. And the result limits surfaces is the same as that with the original method, and they are both smooth surfaces.